In a solid crystal, a periodic potential distribution of atomic nuclei exhibits interference with an electron wave at a wavelength corresponding to the lattice constant. Namely, when the wavelength of an electron wave is close to the potential period of a crystal, reflection occurs due to three-dimensional diffraction (Bragg diffraction). This phenomenon forbids the passage of electrons contained in a specified energy region. This forms an electronic band gap used for semiconductor devices and the like.
Similarly, a three-dimensional structure periodically changing in refractive index or dielectric constant exhibits interference with electromagnetic waves and cuts off electromagnetic waves in a specified frequency region. In this case, a forbidden band is referred to as a “photonic band gap”, and the three-dimensional structure is referred to as a “photonic crystal”.
By using the above-described action, the photonic crystal is possibly used as a cut-off filter for cutting off transmission of electromagnetic waves in a predetermined frequency region, or as a waveguide or a resonator in which a heterogeneous portion, which disturbs periodicity, is introduced into the periodic structure, for trapping light or an electromagnetic wave in the portion. Also, the photonic crystal is possibly applied to an ultralow-threshold laser for light, a high-directivity antenna for electromagnetic waves, or the like.
When Bragg diffraction of an electromagnetic wave occurs in the photonic crystal, two types of standing waves are generally formed. FIG. 6 shows the two types of standing waves. The standing wave shown in FIG. 6A has high vibration energy in a region with a low dielectric constant, and the standing wave shown in FIG. 6B has high vibration energy in a region with a high dielectric constant. A wave at an energy level between the two standing waves split into two different modes is not allowed to be present in the crystal, thereby causing a band gap.
The photonic crystal has a one-, two-, or three-dimensional structure, but a three-dimension structure is required for obtaining a complete photonic band gap.
Examples of a method for forming a three-dimensional structure include a method using a square timber stacked film (Patent Documents 1 and 2) or a shape-preserving multilayer film utilizing auto-cloning (Patent Document 3), a method using optical molding (Patent Documents 4 and 5), and a method of arranging particles (Patent Document 6). These documents disclose a technique for forming a photonic crystal by processing an insulator, a dielectric material, or a semiconductor material such as an organic material, ceramic, Si, or the like. Also, a three-dimensional structure formed by curing a mixture containing a resin composition and dielectric particles is disclosed (Patent Document 7).                [Patent Document 1] PCT Japanese Translation Patent Publication No. 2001-518707        [Patent Document 2] Japanese Unexamined Patent Application Publication No. 2001-74955        [Patent Document 3] Japanese Unexamined Patent Application Publication No. 2001-74954        [Patent Document 4] Japanese Unexamined Patent Application Publication No. 2000-341031        [Patent Document 5] PCT Japanese Translation Patent Publication No. 2001-502256        [Patent Document 6] Japanese Unexamined Patent Application Publication No. 2001-42144        [Patent Document 7] Japanese Unexamined Patent Application Publication No. 2001-261977        
It is known that a photonic band gap obtained in such a photonic crystal widens as the contrast between the dielectric constants or refractive indexes of two constituent materials increases.
However, the limits of dielectric constants and refractive indexes of the above-described practical materials are about 15 and 3.0, respectively, for example, in a frequency band of 10 to 30 GHz. It is thus difficult to further increase the difference (or ratio) between the dielectric constants or refractive indexes of air and these materials. Therefore, a wide photonic band gap cannot be obtained using a three-dimensional periodic structure composed of a dielectric material having a constant dielectric constant.
A conceivable method for resolving this problem is to widen a band gap by combining periodic structures having various band gaps. Namely, as disclosed in Patent Document 4, an effective method comprises forming a structure by optically molding a photocurable resin containing a ceramic dielectric material dispersed therein or arranging solids each containing a ceramic dielectric material dispersed therein to form a crystal in which the lattice constant continuously changes or the dielectric constant changes. However, some ceramic materials to be dispersed inhibit curing of the photocurable resin and transmittance, thereby causing difficulty in optical molding. Therefore, usable materials are limited, and thus the amount of the ceramic dielectric material dispersed is also limited.
In order to resolve this problem, the method disclosed in Patent Document 7 is also effective, in which a mixture containing a resin composition and dielectric particles is cured. However, a dielectric material is compounded and thus liable to decrease in dielectric constant. The method comprising arranging thermosetting resin or thermoplastic resin blocks containing a ceramic dielectric material dispersed therein to form a structure has difficulty in forming a complicated structure such as a diamond structure.
On the other hand, Patent Document 5 discloses the method in which a resin structure formed by optical molding is impregnated with a resin containing high-dielectric-constant ceramic dispersed therein to form a photonic crystal. However, a wide photonic band gap cannot be formed based on only the contents disclosed in Patent Document 5.
Accordingly, an object of the present invention is to provide a three-dimensional periodic structure having a wide photonic band gap, which could not be obtained in a conventional structure, and a method for producing the structure.